I would be selling the house and purchasing the next, no desire to attempt to become a landlord at this stage.
I am surprised you would need 20% cash on hand to pay the deposit, surely that comes from the equity in the house to be sold? I understand you'll need the booking deposit (which was certainly less than 10% for my current house!).
So sounds like keep a chunk of cash savings for the likes of booking deposit etc but OK to put the bulk to work against the mortgage over the next while.